Details

analyze656.0ms (7.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	154
1	43	154
0	4	4
1	4	4

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Symmetry

Compiler

Compiled 16 to 12 computations (25% saved)

sample25.0ms (0.3%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	17×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	22
1	16	22

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

27.0b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.3b	(+.f64 (.f64 a c) (.f64 b d))
26.4b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite73.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

26.8b

Rules

10×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
9×	`times-frac_binary64_2130`
4×	`add-exp-log_binary64_2162` `add-log-exp_binary64_2163` `add-cbrt-cube_binary64_2160`
3×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `associate-/l_binary64_2069` `associate-/r_binary64_2068`
2×	`pow1_binary64_2185` `associate-/l/_binary64_2071` `associate-/r/_binary64_2070`
1×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `div-inv_binary64_2121` `sum-log_binary64_2215` `+-commutative_binary64_2054`

Counts

2 → 42

Calls

2 calls:

9.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))

Compiler

Compiled 1203 to 160 computations (86.7% saved)

series461.0ms (5.1%)

Error

6.3b

Counts

2 → 48

Calls

2 calls:

285.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
142.0ms	(+.f64 (.f64 a c) (.f64 b d))

Compiler

Compiled 1644 to 1011 computations (38.5% saved)

simplify49.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5127	1791

prune76.0ms (0.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	83	7	90
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	83	8	91

Error

6.2b

Counts

91 → 8

Compiler

Compiled 1827 to 244 computations (86.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (.f64 d b) (.f64 c a))
18.4b	(/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
30.5b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
30.5b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite116.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

6.2b

Rules

23×	`add-sqr-sqrt_binary64_2146`
21×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
18×	`sqrt-prod_binary64_2140` `times-frac_binary64_2130`
6×	`pow1_binary64_2185` `add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `sqrt-div_binary64_2141` `associate-/r*_binary64_2068`
5×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
3×	`associate-/l*_binary64_2069`
2×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `associate-/l/_binary64_2071` `associate-/r/_binary64_2070`
1×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `div-inv_binary64_2121` `sum-log_binary64_2215` `+-commutative_binary64_2054`

Counts

4 → 84

Calls

4 calls:

10.0ms	(/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 d b) (.f64 c a))

Compiler

Compiled 3211 to 343 computations (89.3% saved)

series898.0ms (9.9%)

Error

6.2b

Counts

4 → 93

Calls

4 calls:

401.0ms	(/.f64 (+.f64 (.f64 d b) (.f64 c a)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
153.0ms	(+.f64 (.f64 d b) (.f64 c a))
129.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
124.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 5880 to 3131 computations (46.8% saved)

simplify93.0ms (1%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4980	3620
1	4980	3620

prune163.0ms (1.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	173	4	177
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	176	9	185

Error

6.2b

Counts

185 → 9

Compiler

Compiled 5358 to 778 computations (85.5% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.3b	(+.f64 (.f64 a c) (.f64 b d))
0.8b	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
26.2b	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))

rewrite119.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

6.2b

Rules

26×	`add-sqr-sqrt_binary64_2146`
20×	`*-un-lft-identity_binary64_2124` `times-frac_binary64_2130`
19×	`add-cube-cbrt_binary64_2159`
16×	`add-exp-log_binary64_2162`
15×	`associate-r_binary64_2064`
10×	`add-cbrt-cube_binary64_2160`
6×	`pow1_binary64_2185`
5×	`add-log-exp_binary64_2163` `flip3-+_binary64_2127` `flip-+_binary64_2098`
4×	`div-exp_binary64_2175` `prod-exp_binary64_2173` `associate-/r/_binary64_2070`
3×	`unswap-sqr_binary64_2092` `associate-l_binary64_2065` `associate-/l_binary64_2069` `associate-/r_binary64_2068`
2×	`1-exp_binary64_2168` `rec-exp_binary64_2174` `cbrt-unprod_binary64_2157` `cbrt-undiv_binary64_2158` `frac-times_binary64_2134` `associate-*l/_binary64_2067` `div-inv_binary64_2121`
1×	`pow-prod-down_binary64_2195` `un-div-inv_binary64_2122` `associate-r/_binary64_2066` `-commutative_binary64_2055` `inv-pow_binary64_2209` `pow-flip_binary64_2198` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `sum-log_binary64_2215` `+-commutative_binary64_2054`

Counts

3 → 86

Calls

3 calls:

16.0ms	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))
7.0ms	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))

Compiler

Compiled 2473 to 595 computations (75.9% saved)

series534.0ms (5.9%)

Error

6.2b

Counts

3 → 57

Calls

3 calls:

286.0ms	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))
148.0ms	(+.f64 (.f64 a c) (.f64 b d))
63.0ms	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 2196 to 1469 computations (33.1% saved)

simplify76.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5349	2564

prune110.0ms (1.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	143	9	152

Error

6.2b

Counts

152 → 9

Compiler

Compiled 3077 to 659 computations (78.6% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (+.f64 (.f64 d b) (.f64 c a)) (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
18.5b	(.f64 (+.f64 (.f64 d b) (.f64 c a)) (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))))
30.5b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
30.5b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite342.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

6.2b

Rules

54×	`associate-r_binary64_2064`
45×	`add-exp-log_binary64_2162`
44×	`times-frac_binary64_2130`
43×	`add-sqr-sqrt_binary64_2146`
35×	`add-cbrt-cube_binary64_2160` `add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
28×	`sqrt-prod_binary64_2140`
20×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
18×	`cbrt-prod_binary64_2155`
13×	`pow1_binary64_2185`
11×	`frac-times_binary64_2134` `associate-*l/_binary64_2067`
10×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `div-exp_binary64_2175` `cbrt-undiv_binary64_2158`
8×	`sqrt-div_binary64_2141`
4×	`add-log-exp_binary64_2163` `pow-prod-down_binary64_2195` `associate-r/_binary64_2066` `associate-l*_binary64_2065` `associate-/r/_binary64_2070`
3×	`unswap-sqr_binary64_2092`
2×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `div-inv_binary64_2121` `*-commutative_binary64_2055`

Counts

4 → 148

Calls

4 calls:

29.0ms	(.f64 (.f64 (+.f64 (.f64 d b) (.f64 c a)) (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
19.0ms	(.f64 (+.f64 (.f64 d b) (.f64 c a)) (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 7558 to 2406 computations (68.2% saved)

series1.1s (12.6%)

Error

6.2b

Counts

4 → 93

Calls

4 calls:

431.0ms	(.f64 (+.f64 (.f64 d b) (.f64 c a)) (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))))
309.0ms	(.f64 (.f64 (+.f64 (.f64 d b) (.f64 c a)) (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
146.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
142.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 6297 to 4314 computations (31.5% saved)

simplify123.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4970	6617
1	4970	6617

prune293.0ms (3.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	239	2	241
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	240	10	250

Error

5.0b

Counts

250 → 10

Compiler

Compiled 8158 to 2446 computations (70% saved)

regimes1.4s (15.1%)

Accuracy

Total 10.4b remaining (68.4%)

Threshold costs 0b (0%)

Compiler

Compiled 10414 to 5923 computations (43.1% saved)

bsearch117.0ms (1.3%)

Steps

Iters	Range		Point
7	4.117858648655341e+91	1.9723673895504925e+93	4.762697302129139e+91
10	1.5231040203580734e+36	9.243221395213837e+47	5.454863883134953e+45
10	6.555227830381637e-178	2.086040430058216e-159	1.0481161816497777e-159
8	-2.046786059085387e-135	-1.2731732764803528e-139	-1.1669216222378627e-135
7	-5.654621146319898e+146	-2.3454933525060197e+145	-2.5033965365909377e+145

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	170
1	47	170

Removed

()

end0.0ms (0%)

sample2.1s (23.7%)

Algorithm

1×

intervals

Results

357.0ms	8000×	body	128	valid
18.0ms	432×	body	128	invalid

Compiler

Compiled 2206 to 1233 computations (44.1% saved)

Details

analyze656.0ms (7.3%)

sample25.0ms (0.3%)

simplify7.0ms (0.1%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite73.0ms (0.8%)

series461.0ms (5.1%)

simplify49.0ms (0.5%)

prune76.0ms (0.8%)

localize15.0ms (0.2%)

rewrite116.0ms (1.3%)

series898.0ms (9.9%)

simplify93.0ms (1%)

prune163.0ms (1.8%)

localize12.0ms (0.1%)

rewrite119.0ms (1.3%)

series534.0ms (5.9%)

simplify76.0ms (0.8%)

prune110.0ms (1.2%)

localize17.0ms (0.2%)

rewrite342.0ms (3.8%)

series1.1s (12.6%)

simplify123.0ms (1.4%)

prune293.0ms (3.2%)

regimes1.4s (15.1%)

bsearch117.0ms (1.3%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.1s (23.7%)

Profiling